For a given payoff matrix, we use the replicator equation to model the evolutionary dynamics among learning rules [1]}. The equation tracks the frequencies of each learning rule over time, and it favors those rules with higher average payoffs (see Methods). For \(2\times 2\)  games, as in our case, replicator dynamics can result in four qualitatively different scenarios [2]}, [3]}. Either one learning rule is globally stable (dominance), there is a mixed population that is globally stable (coexistence), both learning rules are locally stable (bistability), or any mixed population is stable (neutrality).
